An Ergodic Theorem for the Symmetric Generalized Exclusion Process

#### J.D. Keisling

1998, v.4, №3, 351-379

ABSTRACT

The $N$-exclusion process is an interacting particle system that generalizes the simple exclusion process by allowing up to N particles at each site. In this paper, we define the jump rates to be 1 if any particles are present and 0 if not, and we consider the infinite-volume limit of this process in arbitrary dimension. Assuming symmetry and translation invariance of the underlying Markov chain, we show that the extremal translation-invariant stationary measures are product measures, one for each given density'' of particles. With the further assumption of irreducibility, we generalize a coupling argument of Liggett to show that every translation-invariant measure converges to a mixture of these product measures.

Keywords: generalized exclusion process,ergodic theorem,stationary measures,coupling,interacting particle system